Simulation of second harmonic generation enhancement in metal micro-nano dimers excited by femtosecond vortex beams (<italic>invited</italic>)

ObjectiveSecond Harmonic Generation (SHG) plays a pivotal role in novel coherent light sources, high-sensitivity biosensing, and all-optical signal processing. However, as photonic devices scale down to the sub-wavelength regime, traditional nonlinear crystals face significant efficiency bottlenecks due to the reduced interaction volume, hindering their application in integrated nanophotonics. Localized Surface Plasmon Resonance (LSPR) in metal nanostructures offers a solution by confining light into sub-wavelength regions to enhance the local electric field. While continuous waves and Gaussian beams have been extensively studied, the transient dynamics and field manipulation capabilities of femtosecond vortex beams—carrying Orbital Angular Momentum (OAM)—interacting with metal nanostructures remain less explored. This study aims to propose a method for enhancing and manipulating SHG by exciting metal micro-nano dimers with femtosecond vortex pulses. By investigating the coupling between the spiral phase of vortex beams and the LSPR modes of metal dimers, this work seeks to reveal the mechanism of spatiotemporal evolution of nonlinear signals and provide a theoretical basis for designing efficient, miniaturized on-chip nonlinear light sources.MethodsA transient electromagnetic field model is established to simulate the interaction between femtosecond vortex pulses and metal micro-nano dimers placed on a nonlinear material substrate (Lithium Niobate). The Finite Element Method (FEM) is employed for numerical calculations. The dispersion characteristics of the gold material are described using the Drude-Lorentz model to accurately represent the broadband optical response, including intraband electron motion and interband transitions. The nonlinear response of the substrate is characterized by a residual electric displacement field model. The study systematically investigates two types of nanodimer structures: spherical gold dimers and ellipsoidal gold dimers. The simulation domain utilizes Perfect Magnetic Conductor (PMC) boundaries for the upper and lower interfaces and Scattering Boundary Conditions (SBC) for the outer boundaries to simulate infinite space propagation. Key geometric parameters, including the radius of the spheres, the gap distance between particles, the semi-major axis of the ellipsoids, and their orientation angles relative to the incident polarization, are optimized to maximize the SHG enhancement factor.Results and DiscussionsThe simulation results demonstrate that the introduction of metal micro-nano dimers significantly enhances the local electric field intensity compared to the case without metal structures. Time-domain analysis reveals that the SHG signal experiences a rapid growth phase as the pulse peak enters the structure, reaching saturation due to energy conservation (Fig.2). Frequency-domain analysis confirms that the presence of metal dimers boosts the SHG signal intensity by approximately 3 times under initial unoptimized parameters (Fig.3). Through geometric optimization, the enhancement effect is further amplified. For spherical micro-nano dimers, optimizing the radius and gap distance leads to a maximum SHG enhancement of 200 times. The results indicate that while the gap distance influences the coupling efficiency, the radius is the dominant factor in tuning the LSPR resonance to match the excitation or harmonic frequencies (Fig.4). For ellipsoidal micro-nano dimers, the introduction of shape anisotropy provides additional degrees of freedom. By adjusting the length of the semi-major axis and the orientation angle of the dimers, a "quasi-periodic" oscillation of the enhancement factor is observed. This is attributed to the periodic spectral overlapping between the longitudinal plasmon modes and the harmonic frequencies, as well as the phase interference between coupled fields. Under optimal conditions (semi-major axis matching the resonance and specific orientation angle), the SHG enhancement factor reaches up to 600 times (Fig.5). Furthermore, the interaction between the femtosecond vortex beam and the micro-nano dimers induces a unique near-field distribution. Unlike Gaussian beams, the vortex beam, characterized by its spiral wavefront, breaks the azimuthal symmetry of the excitation. This results in a distinctive "petal-like" field distribution pattern in the gap region of the dimers, exhibiting high-order symmetry (Fig.6). This pattern is highly tunable; by manipulating the geometric parameters of the dimers, such as the gap size and ellipsoid aspect ratio, the clarity and number of these "petals" can be precisely controlled (Fig.7). This phenomenon confirms that the OAM of the vortex beam is effectively transferred to the near-field distribution through mode hybridization.ConclusionsThis study successfully demonstrates that femtosecond vortex beams can significantly enhance and modulate SHG in metal micro-nano dimers. By optimizing the geometry of spherical and ellipsoidal dimers, SHG enhancement factors of 200 and 600 are achieved, respectively. The study reveals a novel "petal-like" near-field distribution mechanism, originating from the coupling between the vortex beam's OAM and the nanostructure's LSPR modes. These findings provide a new pathway for developing integrated nonlinear light sources and offer flexible methods for sub-wavelength light field manipulation, which has potential applications in super-resolution imaging and optical information processing.